Getting More Information About a Clustering¶
Once you have the basics of clustering sorted you may want to dig a little deeper than just the cluster labels returned to you. Fortunately, the hdbscan library provides you with the facilities to do this. During processing HDBSCAN* builds a hierarchy of potential clusters, from which it extracts the flat clustering returned. It can be informative to look at that hierarchy, and potentially make use of the extra information contained therein.
Suppose we have a dataset for clustering. It is a binary file in NumPy format and it can be found at https://github.com/lmcinnes/hdbscan/blob/master/notebooks/clusterable_data.npy.
import hdbscan import numpy as np import matplotlib.pyplot as plt import seaborn as sns %matplotlib inline
data = np.load('clusterable_data.bin') #or data = np.load('clusterable_data.npy') #depending on the format of the file
array([[-0.12153499, -0.22876337], [-0.22093687, -0.25251088], [ 0.1259037 , -0.27314321], ..., [ 0.50243143, -0.3002958 ], [ 0.53822256, 0.19412199], [-0.08688887, -0.2092721 ]])
plt.scatter(*data.T, s=50, linewidth=0, c='b', alpha=0.25)
<matplotlib.collections.PathCollection at 0x7f6b61ad6e10>
We can cluster the data as normal, and visualize the labels with different colors (and even the cluster membership strengths as levels of saturation)
clusterer = hdbscan.HDBSCAN(min_cluster_size=15).fit(data) color_palette = sns.color_palette('deep', 8) cluster_colors = [color_palette[x] if x >= 0 else (0.5, 0.5, 0.5) for x in clusterer.labels_] cluster_member_colors = [sns.desaturate(x, p) for x, p in zip(cluster_colors, clusterer.probabilities_)] plt.scatter(*data.T, s=50, linewidth=0, c=cluster_member_colors, alpha=0.25)
The question now is what does the cluster hierarchy look like – which
clusters are near each other, or could perhaps be merged, and which are
far apart. We can access the basic hierarchy via the
attribute of the clusterer object.
<hdbscan.plots.CondensedTree at 0x10ea23a20>
We can now see the hierarchy as a dendrogram, the width (and color) of
each branch representing the number of points in the cluster at that
level. If we wish to know which branches were selected by the HDBSCAN*
algorithm we can pass
select_clusters=True. You can even pass a
selection palette to color the selections according to the cluster
clusterer.condensed_tree_.plot(select_clusters=True, selection_palette=sns.color_palette('deep', 8))
From this, we can see, for example, that the yellow cluster at the
center of the plot forms early (breaking off from the pale blue and
purple clusters) and persists for a long time. By comparison the green
cluster, which also forms early, quickly breaks apart and then
vanishes altogether (shattering into clusters all smaller than the
min_cluster_size of 15).
You can also see that the pale blue cluster breaks apart into several subclusters that in turn persist for quite some time – so there is some interesting substructure to the pale blue cluster that is not present, for example, in the dark blue cluster.
If this was a simple visual analysis of the condensed tree can tell you
a lot more about the structure of your data. This is not all we can do
with condensed trees, however. For larger and more complex datasets the
tree itself may be very complex, and it may be desirable to run more
interesting analytics over the tree itself. This can be achieved via
several converter methods:
First we’ll consider
<networkx.classes.digraph.DiGraph at 0x11d8023c8>
As you can see we get a NetworkX directed graph, which we can then use all the regular NetworkX tools and analytics on. The graph is richer than the visual plot above may lead you to believe, however:
g = clusterer.condensed_tree_.to_networkx() g.number_of_nodes()
The graph actually contains nodes for all the points falling out of
clusters as well as the clusters themselves. Each node has an associated
size attribute and each edge has a
weight of the lambda value
at which that edge forms. This allows for much more interesting
Next, we have the
to_pandas() method, which returns a panda DataFrame
where each row corresponds to an edge of the NetworkX graph:
parent denotes the id of the parent cluster, the
the id of the child cluster (or, if the child is a single data point
rather than a cluster, the index in the dataset of that point), the
lambda_val provides the lambda value at which the edge forms, and
child_size provides the number of points in the child cluster.
As you can see the start of the DataFrame has singleton points falling
out of the root cluster, with each
child_size equal to 1.
If you want just the clusters, rather than all the individual points
as well, simply select the rows of the DataFrame with
greater than 1.
tree = clusterer.condensed_tree_.to_pandas() cluster_tree = tree[tree.child_size > 1]
Finally we have the
to_numpy() function, which returns a numpy record
array([(2309, 2048, 5.016525967983049, 1), (2309, 2006, 5.076503128308643, 1), (2309, 2024, 5.279133057912248, 1), ..., (2318, 1105, 86.5507370650292, 1), (2318, 965, 86.5507370650292, 1), (2318, 954, 86.5507370650292, 1)], dtype=[('parent', '<i8'), ('child', '<i8'), ('lambda_val', '<f8'), ('child_size', '<i8')])
This is equivalent to the pandas DataFrame but is in pure NumPy and hence has no pandas dependencies if you do not wish to use pandas.